Pearson Physics - Tipp City · Describing Motion • A frame of reference is referred to as a coordinate system. • A coordinate system in one dimension is represented by an x axis

Chapter 2 Lecture

Pearson Physics

Introduction to

Motion

Prepared by

Chris Chiaverina

© 2014 Pearson Education, Inc.

Chapter Contents

• Describing Motion

• Speed and Velocity

• Position-Time Graphs

• Equation of Motion


Describing Motion

• A frame of reference is referred to as a

coordinate system.

• A coordinate system in one dimension is

represented by an x axis with the origin located

at x = 0.

• Once an origin and a positive direction are

chosen, they must be used consistently.


Describing Motion

• The letter x is used to label position.

• An arrow drawn from the origin of a coordinate

system to an object is referred to as the object's

position vector.

• Whenever an object is in motion, its position is

changing.


Describing Motion

• Initial and final positions are indicated with xi and

xf, respectively.


Describing Motion

• Distance is the total length of the path taken on

a trip.

– No direction is associated with distance. It is a

scalar quantity.

– The SI unit of distance is the meter (m).

– When walking, distance is measured with a

pedometer.

– In a car, the distance is measured using an

odometer.


Describing Motion

• Displacement is defined as an object's change in

position.

– Displacement is a vector having both

magnitude and direction.

– The SI unit of displacement is the meter (m).

– The sign of the displacement vector indicates

the direction of motion. Motion in the positive

direction has a positive displacement. Motion

in the negative direction produces a negative

displacement.


Describing Motion

• Displacement is represented by the symbol Δx.

• Δx is shorthand for xf – xi. It does not mean Δ

times x.

• Δx is positive when the change in position is in

the positive direction and negative when the

change in position is in the negative direction.


Describing Motion

• Distance is the total length traveled;

displacement is the net change in position.

• An object's displacement is zero when it returns

to its starting point, even though it may have

traveled a considerable distance.


Describing Motion

• Example: The total length traveled in going from

the math classroom to the library and then to the

physics room is 13.0 m, whereas the

displacement is −3.0 m.


Speed and Velocity

• The rate of motion is referred to as speed.

• Speed describes how fast or slow something

moves.

• The average speed is defined as the distance

traveled divided by the elapsed time:

average speed = distance/elapsed time

• The SI units of average speed are meters per

second (m/s).

• Like distance, average speed is always positive.


Speed and Velocity

• An object's average velocity is defined as its

displacement per unit time:

average velocity = displacement/elapsed time

• The SI units of average velocity are meters per

second (m/s).

• The average velocity describes, on average,

how fast something is moving as well as the

average direction in which the object is moving.

• An object moving in the positive direction has a

positive average velocity. An object moving in

the negative direction has a negative average

velocity. © 2014 Pearson Education, Inc.

Position-Time Graphs

• A position-time graph is an alternative way of

representing data in a table.

• On a position-time graph, position data are

plotted on the y axis; time data are plotted on the

x axis.



• Example: Plotting the position and time

contained in a table results in a position-time

graph.



• A best-fit line drawn through data points can be

used to learn additional information about an

object's motion.



• To find position at a time not in original data,

– trace vertically from a given point on time axis

to the straight line, then

– trace sideways until you reach the position

axis.



• The slope of a straight line is equal to its rise

over its run.

• Any two points may be used to calculate the

slope of a straight line.

• On a position-time graph the rise corresponds to

the an object's position and the run to the

elapsed time.



• The slope of a position-time graph equals

average velocity.

• A straight line on a position-time graph

represents motion with constant velocity.



• A straight line on a

position-time graph

can have a positive,

negative, or zero

slope.

– A positive slope

means a positive

velocity.

– A negative slope

means a negative

velocity.

– Zero slope means

zero velocity.



• The greater the slope of a position-time graph,

the greater the velocity.

• The slope of a tangent line to a position-time

graph at a given instant equals the

instantaneous velocity.


Equation of Motion

• The position-time equation of motion gives an

object's position x at any time t if its initial

position and constant velocity are known.

• The position-time equation states that final

position = initial position + (velocity)(elapsed

time), or xf = xi + vt.


Equation of Motion

• The position-time equation of motion gives a

straight line for motion with constant velocity.

• The intercept of the straight line is the initial

position, and its slope is the velocity.


Equation of Motion

• Example: A skateboarder with an initial position

of 1.5 m moves with a constant velocity of

3.0 m/s. What is the position of the

skateboarder?


Equation of Motion

• Solution: Substituting 1.5 m for the initial position

and 3.0 m/s for the constant velocity in the

equation of motion gives the following:

xf = 1.5 m + (3.0 m/s)(2.5 s) = 9.0 m


Equation of Motion

• The equation for a straight line is often written as

y = mx + b, where m is the slope and b is the y

intercept.

• This equation may be also written y = b + mx.


Equation of Motion

• Except for the labels, y = b + mx is the same

equation as the position-time equation of motion,

xf = xi + vt.


Equation of Motion

Position-time graphs intersect when objects have

the same location.


Pearson Physics - Tipp City · Describing Motion • A frame of reference is referred to as a coordinate system. • A coordinate system in one dimension is represented by an x axis

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